关于一道数学虚数方程题

x^3-6x^2+10x-8=0 => (x^3-6x^2+8x)+(2x-8)=0 => x(x^2-6x+8)+2(x-4)=0
=> (x-4)(x^2-2x+2)=0 => (x-4)((x-1)^2+1)=0 => (x-4)((x-1)^2-i^2)=0
=>(x-4)(x-1+i)(x-1-i)=0